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Subroutine MAP_STEEL_INC_POTENCY

  1. Provenance of code.
  2. Purpose of code.
  3. Specification.
  4. Description of subroutine's operation.
  5. References.
  6. Parameter descriptions.
  7. Error indicators.
  8. Accuracy estimate.
  9. Any additional information.
  10. Example of code
  11. Auxiliary subroutines required.
  12. Keywords.
  13. Download source code.
  14. Links.

Provenance of Source Code

S.J. Jones* and H.K.D.H. Bhadeshia,
Phase Transformations Group,
Department of Materials Science and Metallurgy,
University of Cambridge,
Cambridge, U.K.

*Dr S.J. Jones is now with Ford Motor Co. (UK) Ltd.

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Purpose

To calculate the heterogeneous activation energy barrier to nucleation on a spherical substrate such as an inclusion using classical nucleation theory.

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Specification

Language:FORTRAN
Product form:Source code 

  SUBROUTINE MAP_INC_POTENCY(INCGMAX1VOL,GMAX1VOL,
& RI,UFAFENERGY,FAFENERGY,FIENERGY,AIENERGY,AEB,
& AEBHOMOG,FRACHOMAEB)

  DOUBLE PRECISION INCGMAX1VOL,GMAX1VOL,RI,UFAFENERGY,
& FAFENERGY,FIENERGY,AIENERGY,AEB,AEBHOMOG,FRACHOMAEB

  DOUBLE PRECISION PI,RC,TESTIT,PHI,SEPN,PSI,THETA,BETA,
& FUNCTHETA,FUNCPSI,FUNCBETA,VS,VC1,VC2,VC3,XHGT,YHGT,AS,
& AC1,AC2,AC4,AF


  PARAMETER (PI=3.141592654)

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Description

Barritte [2] developed a model for the activation energy barrier to nucleation on a spherical substrate by assuming that the 'wetting' angle is fixed at 90°. This new model removes this assumption.

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References

  1. S.J. Jones, PhD. thesis, University of Cambridge, (1996).
  2. G.S. Barritte, "The microstructure of weld metals in low alloy steels", PhD. thesis, University of Cambridge, (1982).
  3. R.A. Ricks, G.S. Barritte and P.R. Howell, "Influence of second phase particles on diffusional transformations in steels", Solid State Phase Transformations, Proc. Metall. Society of AIME, Pittsburgh, (1981).

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Parameters

Input parameters

Name Type Description
INCGMAX1VOL real maximum possible thermodynamic driving force for nucleation local to the spherical substrate, per unit volume (Jm-3).
GMAX1VOL real maximum possible thermodynamic driving force for nucleation remote from the spherical substrate, per unit volume (Jm-3).
RI real radius of the spherical substrate(m).
UFAFENERGY real interfacial energy per unit area at a disordered boundary between the product and the parent phases (Jm-2 ).
FAFENERGY real interfacial energy per unit area at a facetted (coherent) boundary between the product and the parent phases (Jm-2 ).
FIENERGY real interfacial energy per unit area between the product phase and the spherical substrate (Jm-2 ).
AIENERGY real interfacial energy per unit area between the parent phase and the spherical substrate (Jm-2 ).

Output parameters

Name Type Description
AEB real activation energy barrier to nucleation at the spherical substrate (J).
AEBHOMOG real activation energy barrier to homogeneous nucleation remote from the spherical substrate (J).
FRACHOMAEB real ratio between AEB and AEBHOMOG. This is the effective 'shape' factor for nucleation on the spherical substrate.

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Error Indicators

  1. If FAFENERGY is greater than UFAFENERGY then an error is reported and the program execution is stopped.
  2. If the absolute value of TESTIT is greater than unity then an error is reported and the program execution is stopped.
  3. If YHGT is greater than XHGT then an error is reported and the program execution is stopped.

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Accuracy

No information supplied.

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Further Comments

None.

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Example

1. Program text

      DOUBLE PRECISION GMAX1VOL,RI,UFAFENERGY,FAFENERGY,
     & FIENERGY,AIENERGY,AEB,AEBHOMOG,FRACHOMAEB,INCGMAX1VOL
      READ(*,*) INCGMAX1VOL,GMAX1VOL,RI,UFAFENERGY,FAFENERGY,
     & FIENERGY,AIENERGY
C
      CALL MAP_STEEL_INC_POTENCY(INCGMAX1VOL,GMAX1VOL,RI,UFAFENERGY,
     & FAFENERGY,FIENERGY,AIENERGY,AEB,AEBHOMOG,FRACHOMAEB)
C
      WRITE(*,10) AEB,AEBHOMOG,FRACHOMAEB
10    FORMAT(E10.3,1X,E10.3,1X,E10.3)
      STOP
      END

2. Program data

-0.260E7 -0.260E7 0.270E-6 0.500E-1 0.363E-1 0.463E-1 0.623E-1

3. Program results

0.814E-16 0.310E-15 0.263E0

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Auxiliary Routines

None.

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Keywords

activation, energy, barrier, nucleation, classical, spherical, substrate, inclusion, heterogeneous, homogeneous

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Download

Download source code

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MAP originated from a joint project of the National Physical Laboratory and the University of Cambridge.

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